The paper addresses the problem of efficient identification of the Open Circuit Voltage versus State of Charge (OCV-SOC) dependency for lithium-ion batteries, which is a critical step for creating accurate Battery Management Systems (BMS). Traditional approaches using uniform discretization are characterized by increased time costs and low accuracy, since they do not take into account the shape of the OCV(SOC) curve. This article presents four adaptive discretization algorithms based on local function nonlinearity analysis: second derivative calculation, moving window regression analysis, collinearity analysis via triangle area, and tangent angle variance analysis. The theoretical basis of the developed methods is the principle of interpolation error equidistribution, linking the discretization step to the local function curvature. Numerical simulation was performed using a battery mathematical model with a second-order Thevenin equivalent circuit. Results demonstrate that the proposed algorithms provide approximation accuracy comparable to a fine uniform grid (2 % SOC step). The methods based on the second derivative and regression analysis showed the highest efficiency regarding the accuracy-to-time ratio. The developed approaches include smoothing mechanisms to ensure robustness against measurement noise and are recommended for optimizing battery characterization processes in research and industrial conditions.
This paper studies the production of D∗-mesons in deep inelastic scattering of electrons on protons within the framework of the leading approximation in the strong coupling constant in the collinear parton model and in the parton Reggeization approach. The hadronization of c-quarks is described within the Peterson fragmentation model taking into account the masses of c-quarks and D∗-mesons. The calculations were performed using the KaTie parton level generator and unintegrated parton distribution functions in the modified Kimber – Martin – Ryskin – Watt model. It is shown that the experimental data of the ZEUS and H1 collaborations, obtained at energies √s = 300 − −319 GeV, are in satisfactory agreement with theoretical calculations, with the exception of the region of high D∗-meson pseudorapidity. No significant differences are observed in the predictions of the collinear parton model and the parton Reggeization approach. Predictions are made for various differential cross sections for the production of D∗-mesons at the EIC collider energy, √s = 140 GeV.
In this paper, we consider a nonlocal initial-boundary problem. A distinguishing feature of this problem is the form of nonlocal boundary conditions which are known in scientific literature as Steklov conditions. A large proportion of papers dealing with nonlocal problems with Steklov conditions is devoted to second-order parabolic and hyperbolic equations. In the presented here paper we study the nonlocal problem with Steklov boundary conditions for fourth-order equation and obtain sufficient conditions for unique solvability of it in Sobolev space. The proof of both uniqueness and existence of the solution to the problem under consideration is based on a priori estimates and the properties of Sobolev spaces
We establish continuous dependence on parameters and initial conditions, as well as explicit solution estimates, for fractional differential equations involving the Atangana – Baleanu derivative in the Caputo sense (ABC). Despite the existence of analogous results for the Atangana – Baleanu derivative in the Riemann – Liouville sense (ABR) [13], for the Caputo formulation such results have previously been obtained only for systems with generalised Mittag – Leffler kernels [16]. We fill this gap by proving, for scalar ABC equations with standard Mittag – Leffler kernels, a theorem on equivalent integral formulation, an explicit exponential solution estimate, and theorems on continuous dependence with respect to initial data and parameters. The proofs rest on the representation of the ABC derivative via a Prabhakar-type fractional integral, Krasnoselskii’s fixed-point theorem, and the Gronwall – Bellman inequality
This paper identifies the advantages and disadvantages of the subject-methodological and organizational-didactic potential of artificial-intelligence and neural network-technologies (AI-technologies and neural networks). It examines the risks and challenges associated with the implementation of these technologies in the educational process and analyzes the specifics of their application in mathematics and science education. A list of AI-based applications, services, platforms, and programs used in mathematics and science education is provided, along with a didactic model for the formation and development of the subject-digital culture of undergraduate pedagogical students. Using examples of specific tasks solved using AI-tools, the conditions for the productive use of the subject-methodological and organizational-didactic potential of AI-technologies and neural networks in the teaching of mathematics and computer science are determined. Prospects for using AI-tools as auxiliary organizational-didactic tools used by teachers and students in their daily activities are outlined.
The subject of research in this article is a mobile communication mast (hereinafter referred to as the mast), which allows for the elevation of an antenna device to a height of 14 meters. The mobile communication mast is a versatile and effective structure for use in the fields of security and telecommunications. This mast also has specific applications in the military industry, such as for the installation of antennas, radars, border control cameras, and perimeter surveillance cameras for field camps. In some regions, especially in rural areas or in emergency situations (such as after natural disasters), access to stationary base stations may be limited. This mast can be deployed in a short time, providing communication where it is needed. One of the main advantages of this mast is its ability to be installed on vehicles. This advantage allows it to be used in both mobile and stationary conditions, adapting to the specific needs of each project. Thus, mobile communication mast is a mobile station that provides temporary cellular coverage and bandwidth in areas where additional network resources are needed. The masts can quickly and effectively meet short-term needs for coverage and bandwidth, ensuring users have access to reliable communication services when and where they need them. Testing the mast for strength is necessary to ensure the safety, reliability, and durability of the structure, as well as to prevent accidents and failures in related systems. The testing allows for determining how well the mast can withstand existing and planned loads, as well as identifying the need for reinforcement, replacement of elements, or upgrades.
The initiation of a straight crack at the interface between dissimilar materials is considered. A modified maximum tangential stress (MMTS) criterion is presented to predict the conditions for the initiation of failure in initially straight bimaterial cracks. The criterion takes into account the effect of T-stress on the prediction of fracture toughness in mixed-mode specimens with interface cracks. The formulated criterion enables an analytical investigation of the influence of the sign and magnitude of T-stress on fracture toughness in mixed mode. Finite element method (FEM) was used to obtain stress intensity factors (SIFs) for mode I and mode II fracture, as well as T-stresses, at various geometric parameters of the specimens. The proposed criterion is evaluated using experimental data obtained from fracture tests of a tri-material adhesive joint (double cantilever beam specimen) made of carbon fiber-reinforced composite and steel sheet bonded with epoxy resin. An edge crack was introduced into the «steel/epoxy resin» interface.
In the present work, we considered fully a third-order two-point boundary value problem and developed a fourth-order computational method for the approximate solution of the problem. In the development of the computational algorithm, we considered finite differences and Taylor’s higher order approximations method. The proposed algorithm mirrors the coefficient matrix structure of the second-order accurate algorithm found in existing literature. Hence, we have not initiated a discussion on the convergence of the proposed method to avoid repetition. The efficiency and convergence of the proposed algorithm are established by computational experiment. Numerical results obtained in the computational experiment with model problems approve a fourth order accuracy of the proposed method.
We consider Riccati equation with real coefficients and the roots of the right-hand side with different finite limits both at plus infinity and minus infinity. The structure of the solutions set is studied using a certain operator called discriminant operator. In this paper, we study properties of this operator, as well as provide proofs of some results that were previously used.
The goal of the research is to present the results of algorithms, that enable the detection of various types of anomalous values, and the construction of a Poincar’e ellipse with different color coding for anomalies. To achieve the stated goal, the Wolfram Mathematica computer system is used. This system offers a wide range of capabilities for analyzing anomalous values, using optimized algorithms. The considered functions allow solving real-world problems and creating applications for processing data of various natures, including the detection of anomalous values in samples of different types. The analysis of values revealed non-extreme anomalous values. Ignoring such values or using them in analysis can distort conclusions if these values are not detected and a decision on how to handle them within a specific task is not made. Furthermore, non-extreme anomalous values may indicate new, unexplored patterns. Extreme anomalous values, on the other hand, more often indicate problems in the data collection system or exceptional external events. During processing, such values are almost always removed. Non-extreme anomalies are cleaned if they are errors, or retained and accounted for if they are part of a real phenomenon.
In modern conditions, the development of large reservoirs is at a declining stage of production. To maintain optimal reservoir pressure in productive horizons, the use of reservoir flooding technology is required. Maintaining the design parameters of oil production is associated with the need to intensify sampling by increasing the bottom-hole pressure in the injection well system. At the same time, there is a significant risk of exceeding the critical fracturing pressure, which can initiate the formation of hydraulic fracturing fracks. The spread of hydraulic fracturing causes an increase in the likelihood of premature breakthrough of reservoir waters into the drainage area of the operational well stock, which will lead to an increase in the coefficient of waterlogging of the produced products. The analysis of actual numerical mathematical models of the process of colmation of technogenic fracks made it possible to assess the current state of coupled geomechanical and hydrodynamic approaches to studying the patterns of frack growth, taking into account the processes of colmation of frack boundaries. The relevance of the issue is confirmed by the results of special studies conducted at a number of oil and gas fields aimed at determining the dynamics of the development of hydraulic fracturing. The use of complex geomechanical and hydrodynamic models makes it possible to monitor changes in the linear parameters of a technogenic fracks both when the bottom-hole pressure exceeds the fracturing pressure and during the coloration of its boundaries. As part of the research, a physico-mathematical model of the injection process of the "water – reagent" suspension system into a productive reservoir has been developed, taking into account changes in the static stress-strain state of the rock mass. The aim of the work is to quantify the growth dynamics of the initiated fracturing fracture, taking into account changes in the stress-strain state of the formation and to establish functional relationships between the bottom-hole pressure and the flow rate of the injected suspension water identifying characteristic areas of intensive growth and stabilization of parameters. An integrated geomechanical and hydrodynamic model has been developed that reproduces the sequence of stages of the formation of a tecnogenic frack when a production well is switched to injection mode. Quantitative estimates of the distribution of the settled reagent concentration have been obtained both within the crack and in the crack space, depending on changes in the stress state of the bottom-hole zone of the well
Combustion reactions involving small molecules are well understood. However, when addressing the formation of large soot particles or, conversely, the combustion of solid fuels such as biochar, detailed kinetic modeling becomes unfeasible. Describing these processes is inherently complex and multi-scale. At the molecular level, accurate first-principles quantum chemical methods are required to obtain reliable thermodynamic properties and rate constants for elementary reaction steps. At the (super)nanoscale, classical or coarse-grained force field methods are typically employed. Bridging these scales requires efficient screening tools to identify relevant reactants and reaction pathways for constructing realistic soot formation models. This work presents a brief review of quantum chemistry methods used in the theoretical investigation of solid soot particle precursor formation. The review highlights selected highly cited and recent publications from leading research groups on the recombination, self-recombination, and polymerization of monoaromatic and polycyclic aromatic hydrocarbons (PAHs), and provides a concise assessment of the quantum chemical approaches employed
The article considers the possibility of strengthening the protection of information and computing systems with wireless data transmission channels. The possibility of reducing the level of vulnerability criticality by increasing the secrecy of the OFDM radio signal is shown. Examples of calculating the assessment of the criticality level of vulnerabilities exploited in the implementation of the man–in-the-middle threat for existing Wi-Fi networks and for the same networks in the case of the introduction of a protection mechanism in IEEE 802.11 standards with increased structural secrecy of the OFDM radio signal.
The article addresses the pressing issue of stress field reconstruction in the vicinity of a crack tip based on digital photoelasticity data. The objective of the work is to examine an analytical method based on M. Williams multi-parameter asymptotic expansion alongside modern deep learning methods. The materials and methods include a custom-developed Python software suite for the automated processing of isochromatic patterns, as well as convolutional neural network architectures such as StressNet, StressUnet, PhotoelasNet, and an original U-Net-based model for image interpolation. The study identifies key limitations of the analytical approach, such as high sensitivity to the choice of initial approximations and series truncation errors. While the analysis of neural network models demonstrated high efficiency on synthetic data, it revealed a lack of generalization when working with real experimental data. The discussion proposes a hybrid use of Williams analytical expansion and the neural network approach to enhance the accuracy and physical interpretability of quantitative stress analysis results.
This paper derives calibration formulas for the stress intensity factor (SIF) and T-stresses for a central crack of length 2a in a finite-size anisotropic plate under uniaxial tension perpendicular to the crack. The relevance of the study stems from the need to account for material anisotropy and the influence of plate geometric parameters, such as the crack length to plate width ratio (where l is the half-width of the plate, so the ratio is a/l), on fracture mechanics parameters. The lack of compact analytical formulas for calculating the SIF in finite-size plates hinders the rapid assessment of the strength and residual life of structural elements. An asymptotic expansion of stress fields in the vicinity of a crack tip in an infinite anisotropic plane is presented. Particular attention is paid to the first regular (non-singular) terms of the Williams series and an assessment of their contribution to the stress distribution near the crack tip. An analytical solution to the problem for an anisotropic plate exists; however, it is only valid for infinite dimensions. Therefore, finite element modeling (FEM) is used. Based on a combination of two approaches – analytical (for an infinite plate) and numerical (FEM) – an overdetermined method is used to obtain semianalytical calibration formulas for an anisotropic plate of finite dimensions. The study included a series of numerical simulations using the finite element method. Two parameters were varied: the relative crack length a/l (range from 0.1 to 0.4 with a step of 0.05) and the degree of material anisotropy, expressed as the ratio of the actual shear modulus to its Saint-Venant approximation G12/Gsv12. The resulting calibration formulas are approximated as fourth-degree polynomials and can be directly used in engineering practice to calculate stress intensity factors and T-stresses without additional numerical simulations.
This paper presents an approach to reconstructing the spatial distribution of a pollutant based on measurement data from several monitoring stations. The traditional interpolation by radial basis functions, which depend only on distance, does not allow taking into account the anisotropic nature of the propagation of pollutants in the presence of wind. Instead of the Cartesian distance, it is proposed to calculate the effective distance between points, which is a function of wind direction and speed. Analytical dependencies for calculating the effective distance are obtained and modeling examples are presented
Determining drug dosages when multiple drugs are administered simultaneously is an important, long-standing problem in both practical pharmacokinetics and theoretical modeling. Currently, very simple and mostly linear models are used to describe drug distribution in the body, their function, and elimination. Many processes associated with drug delivery occur on very different time scales. This fact, as well as the presence of rapid direct and reverse binding of the drug to blood proteins, allows us to present in this paper a nonlinear model of intravenous drug delivery as a singularly perturbed system of differential equations. The resulting system is analyzed using the integral manifold method
We establish new relationships between the distribution of roots of entire functions and certain integral characteristics of the logarithms of the modules of these entire functions. These integral characteristics are constructed on the basis of arbitrary trigonometrically convex functions. The integral characteristics themselves are defined as double and iterated integrals over circles centered at the origin and radial intervals. The results make significant use of relatively recently established integral formulas of the Carleman and B.Ya. Levin type for subharmonic functions on regions symmetric with respect to a circle. All the main results are proved first for subharmonic functions on the complex plane and their Riesz mass distributions. Then they are transferred to the logarithms of the modules of entire functions and their distributions of zeros. The established relationships will find applications in the theory of the growth of entire and subharmonic functions and, through known dualities, in approximation problems on subsets of the complex plane.
The paper considers a one-dimensional convection – diffusion – reaction continuous model with boundary conditions of the first kind, as well as mixed boundary conditions of the first and third kind. For numerical analysis and subsequent use to solve discrete-time filtering problems, new discrete-time linear state space models are proposed, obtained by discretizing the initial continuous model with different types of boundary conditions based on an unconditionally positive finite difference scheme. The correctness of the proposed discrete-time models has been verified by the results of a series of numerical experiments. Using computer modeling, a numerical comparison of discrete-time state space models obtained using an unconditionally positive finite difference scheme with the results obtained earlier in the works of other authors has been carried out. Numerical experiments have confirmed the correctness of the constructed discrete-time state space linear models. The obtained results can be used to solve the problem of discrete-time filtering based on incomplete noisy observational data
The work is devoted to the application of the decomposition method of linear systems using matrix Padґe approximations. The study focuses on the capabilities and limitations of traditional approaches to gyroscopic system analysis based on classical precession theory. Detailed calculation results are presented for obtaining a splitting transform for decomposing the system of differential equations under study. The results of finding unknown transformation functions as expansions in powers of a small parameter and as Padґe approximants are presented. The advantage of using Padґe approximations over the standard expansion in the form of a power series is shown, since the proposed method provides an increase in the accuracy of asymptotic formulas without increasing the number of terms in expansions in power series. The effectiveness of the proposed approach is demonstrated using the asymptotic decomposition of the equations of a gyroscopic vertical with radial correction
